England's communities are being "short-changed" by £4.1bn a year under the model used to allocate central government funding across the UK, the Local Government Association has said.

This money needed to be "repatriated", demanded the LGA, which represents councils in England and Wales.

It should then be used to address the "crisis engulfing adult social care", the body argued.

The UK government disputes the LGA analysis.

Analysis

By Mike SergeantLocal government correspondent, BBC News

Council funding is always desperately complicated. Throw in the added dimension of devolution, and the upcoming Scottish referendum: you've got a tangle that the finest financial and political minds will struggle to make sense of.

Joel Barnett's 1970s formula was supposed to be a short-term settlement. Even Lord Barnett himself eventually lost faith in his calculation.

Criticised by the English for being unfair, by the Welsh for doing no favours to Wales and by the Scots for institutionalising Westminster hand-outs, the Barnett formula, it seems, satisfies no-one.

The model used to determine how central government funds are divided up is called the Barnett formula, after former Chief Secretary to the Treasury Lord Barnett.

Critics note that the formula is based on population and not need.

LGA chairman Sir Merrick Cockell said: "The Barnett formula has passed its use-by date. It is an historic relic from a time when the government stopped people taking more than £50 on a holiday abroad.

"What was only ever intended as a stop-gap solution has now become a major problem which is short-changing English communities and underfunding their public services by £4.1bn a year."

'Cemented'

He argued that a "fair and equitable distribution of public money" across the UK was now needed.

"The crisis engulfing adult social care demands a shift to a needs-based formula for distributing funding," Sir Merrick continued.

"Our ageing population means that there is an enormous increase in demand for council-run adult social services, which must be met to ensure people retain dignity as they get older.

"The major political parties should all make the introduction of a needs-based formula a cornerstone of their pre-election manifestos and the chancellor should look to lay the groundwork for it in his Autumn Statement."

Debate on the Barnett formula goes to the heart of the debate on Scottish independence.

Fair funding?

Many in Scotland would say that comparing the sums that English and Scottish councils get from the Treasury is like comparing apples with pears.

Wales would receive an additional £300m a year were it to be funded like an English region, according to calculations made four years ago by a commission chaired by economist Gerry Holtham.

Councils in Wales have so far been protected from the scale of cuts local authorities across the border in England have experienced, though that is likely to change.

Local government in Northern Ireland has relatively few powers in comparison to elsewhere in the UK.

And Northern Ireland appears to do well under the Barnett formula - for every £1 spent by government in the UK as a whole, each person in Northern Ireland receives about an additional 20p.

But the NI Executive is critical of the Barnett formula for not factoring in any assessment of needs.

Nationalists argue Scotland gets a raw deal from the Barnett formula, but some unionists believe the formula needs changing to give Scotland more financial powers.

The Welsh government also believes it is not well served by Barnett.

Welsh ministers advocate a new needs-based formula, taking into account such things as the age of the population and poverty levels.

The Northern Ireland Executive says it is difficult to assess whether the level of funding it receives under the formula is fair.

The LGA said that England's ageing population was increasing demand for council-run adult social care services by 3% each year, meaning councils would have to find an extra £400m per annum.

Meanwhile councils' central funding was "being cut by 43%", the LGA claimed, "placing social services under enormous strain and leading to reductions in services and a tightening of eligibility criteria".

The UK government disputes the LGA's analysis, arguing that central government funding cuts are offset by increases in "spending power".

This term encompasses a number of factors, including the retention by councils of a higher proportion of taxes levied on local businesses, and "bonus" funds for councils that approve the construction of new homes.